Q. The area of the region bounded by $y = 2x - x^{2}$and the $x$-axis is
A) $\frac{8}{3}\ sq\ units$
B) $\frac{4}{3}\ sq\ units$
C) $\frac{7}{3}\ sq\ units$
D) $\frac{2}{3}\ sq\ units$
Explanation
(b)
Given curve can be rewritten as
$(x - 1)^{2} = - (y - 1)$
[image:8_image26.jpeg]
The curve cut the $x$-axis at (0,0) and (2,0)
$\therefore Required\ area = \ \int_{0}^{2}{\left( 2x - x^{2} \right)dx}$
$= \left\lbrack x^{2} - \frac{x^{3}}{3} \right\rbrack_{0}^{2}$
$= \frac{4}{3}\ sq\ units$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.